I don't have month-by-month data in front of me, but the massive population movements started several months before Merkel's open-borders moment. Why did Syrians in particular decide last year, in huge numbers, to abandon (or monetize) everything they had and take a gamble on Europe? Because their situation was desperately bad and deteriorating, with no prospect of improvement : ever-worsening multi-cornered civil war, and strategic stalemate.
Sure, the movement was no doubt prolonged by the open-borders moment. But to portray it as caused by Merkel's pronouncements is, as politely as possible, non-truthful.

European Tribune - Culture Wars or Globalization for make Great Benefit Glorious Nation of ...

As to the effects on Brexit, one can sure argue that Merkel's policies were not that significant

That wasn't my argument.  

_{It is rightly acknowledged that people of faith have no monopoly of virtue - Queen Elizabeth II}